Purity, spectra and localisation /:
It is possible to associate a topological space to the category of modules over any ring. This space, the Ziegler spectrum, is based on the indecomposable pure-injective modules. Although the Ziegler spectrum arose within the model theory of modules and plays a central role in that subject, this boo...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York :
Cambridge University Press,
2009.
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications ;
v. 121. |
| Schlagworte: | |
| Online-Zugang: | DE-862 DE-863 |
| Zusammenfassung: | It is possible to associate a topological space to the category of modules over any ring. This space, the Ziegler spectrum, is based on the indecomposable pure-injective modules. Although the Ziegler spectrum arose within the model theory of modules and plays a central role in that subject, this book concentrates specifically on its algebraic aspects and uses. The central aim is to understand modules and the categories they form through associated structures and dimensions, which reflect the complexity of these, and similar, categories. The structures and dimensions considered arise particularly through the application of model-theoretic and functor-category ideas and methods. Purity and associated notions are central, localisation is an ever-present theme and various types of spectrum play organising roles. This book presents a unified, coherent account of material which is often presented from very different viewpoints and clarifies the relationships between these various approaches. |
| Beschreibung: | 1 online resource (xxviii, 769 pages) |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9781139649308 1139649302 9781139644242 1139644246 9781139638845 113963884X 9781139641685 1139641689 1139887092 9781139887090 1139635409 9781139635400 1139637541 9781139637541 1139648349 9781139648349 |
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Datensatz im Suchindex
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| adam_text | |
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| author | Prest, Mike |
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| collection | ZDB-4-EBA |
| contents | Pp conditions -- Purity -- Pp-pairs and definable subcategories -- Pp-types and pure-injectivity -- The Ziegler spectrum -- Rings of definable scalars -- M-dimension and width -- Examples -- Ideals in mod-R -- Finitely presented functors -- Serre subcategories and localisation -- The Ziegler spectrum and injective functors -- Dimensions -- The Zariski spectrum and the sheaf of definable scalars -- Artin algebras -- Finitely accessible and presentable additive categories -- Spectra of triangulated categories -- Definable categories and interpretation functors. |
| ctrlnum | (OCoLC)852896207 |
| dewey-full | 511.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3 |
| dewey-search | 511.3 |
| dewey-sort | 3511.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn852896207 |
| illustrated | Not Illustrated |
| indexdate | 2025-04-11T08:41:29Z |
| institution | BVB |
| isbn | 9781139649308 1139649302 9781139644242 1139644246 9781139638845 113963884X 9781139641685 1139641689 1139887092 9781139887090 1139635409 9781139635400 1139637541 9781139637541 1139648349 9781139648349 |
| language | English |
| oclc_num | 852896207 |
| open_access_boolean | |
| owner | MAIN DE-862 DE-BY-FWS DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-862 DE-BY-FWS DE-863 DE-BY-FWS |
| physical | 1 online resource (xxviii, 769 pages) |
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| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | Encyclopedia of mathematics and its applications ; |
| series2 | Encyclopedia of mathematics and its applications ; |
| spelling | Prest, Mike. Purity, spectra and localisation / Mike Prest. Cambridge ; New York : Cambridge University Press, 2009. 1 online resource (xxviii, 769 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Encyclopedia of mathematics and its applications ; v. 121 Includes bibliographical references and index. Pp conditions -- Purity -- Pp-pairs and definable subcategories -- Pp-types and pure-injectivity -- The Ziegler spectrum -- Rings of definable scalars -- M-dimension and width -- Examples -- Ideals in mod-R -- Finitely presented functors -- Serre subcategories and localisation -- The Ziegler spectrum and injective functors -- Dimensions -- The Zariski spectrum and the sheaf of definable scalars -- Artin algebras -- Finitely accessible and presentable additive categories -- Spectra of triangulated categories -- Definable categories and interpretation functors. Print version record. It is possible to associate a topological space to the category of modules over any ring. This space, the Ziegler spectrum, is based on the indecomposable pure-injective modules. Although the Ziegler spectrum arose within the model theory of modules and plays a central role in that subject, this book concentrates specifically on its algebraic aspects and uses. The central aim is to understand modules and the categories they form through associated structures and dimensions, which reflect the complexity of these, and similar, categories. The structures and dimensions considered arise particularly through the application of model-theoretic and functor-category ideas and methods. Purity and associated notions are central, localisation is an ever-present theme and various types of spectrum play organising roles. This book presents a unified, coherent account of material which is often presented from very different viewpoints and clarifies the relationships between these various approaches. English. Logic, Symbolic and mathematical. http://id.loc.gov/authorities/subjects/sh85078115 Categories (Mathematics) http://id.loc.gov/authorities/subjects/sh85020992 Logique symbolique et mathématique. Catégories (Mathématiques) MATHEMATICS Infinity. bisacsh MATHEMATICS Logic. bisacsh Categories (Mathematics) fast Logic, Symbolic and mathematical fast Modultheorie gnd http://d-nb.info/gnd/4170336-4 Modulkategorie gnd http://d-nb.info/gnd/4170335-2 Print version: Prest, Mike. Purity, spectra and localisation. Cambridge ; New York : Cambridge University Press, 2009 9780521873086 (DLC) 2009281037 (OCoLC)286434473 Encyclopedia of mathematics and its applications ; v. 121. http://id.loc.gov/authorities/names/n42010632 |
| spellingShingle | Prest, Mike Purity, spectra and localisation / Encyclopedia of mathematics and its applications ; Pp conditions -- Purity -- Pp-pairs and definable subcategories -- Pp-types and pure-injectivity -- The Ziegler spectrum -- Rings of definable scalars -- M-dimension and width -- Examples -- Ideals in mod-R -- Finitely presented functors -- Serre subcategories and localisation -- The Ziegler spectrum and injective functors -- Dimensions -- The Zariski spectrum and the sheaf of definable scalars -- Artin algebras -- Finitely accessible and presentable additive categories -- Spectra of triangulated categories -- Definable categories and interpretation functors. Logic, Symbolic and mathematical. http://id.loc.gov/authorities/subjects/sh85078115 Categories (Mathematics) http://id.loc.gov/authorities/subjects/sh85020992 Logique symbolique et mathématique. Catégories (Mathématiques) MATHEMATICS Infinity. bisacsh MATHEMATICS Logic. bisacsh Categories (Mathematics) fast Logic, Symbolic and mathematical fast Modultheorie gnd http://d-nb.info/gnd/4170336-4 Modulkategorie gnd http://d-nb.info/gnd/4170335-2 |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85078115 http://id.loc.gov/authorities/subjects/sh85020992 http://d-nb.info/gnd/4170336-4 http://d-nb.info/gnd/4170335-2 |
| title | Purity, spectra and localisation / |
| title_auth | Purity, spectra and localisation / |
| title_exact_search | Purity, spectra and localisation / |
| title_full | Purity, spectra and localisation / Mike Prest. |
| title_fullStr | Purity, spectra and localisation / Mike Prest. |
| title_full_unstemmed | Purity, spectra and localisation / Mike Prest. |
| title_short | Purity, spectra and localisation / |
| title_sort | purity spectra and localisation |
| topic | Logic, Symbolic and mathematical. http://id.loc.gov/authorities/subjects/sh85078115 Categories (Mathematics) http://id.loc.gov/authorities/subjects/sh85020992 Logique symbolique et mathématique. Catégories (Mathématiques) MATHEMATICS Infinity. bisacsh MATHEMATICS Logic. bisacsh Categories (Mathematics) fast Logic, Symbolic and mathematical fast Modultheorie gnd http://d-nb.info/gnd/4170336-4 Modulkategorie gnd http://d-nb.info/gnd/4170335-2 |
| topic_facet | Logic, Symbolic and mathematical. Categories (Mathematics) Logique symbolique et mathématique. Catégories (Mathématiques) MATHEMATICS Infinity. MATHEMATICS Logic. Logic, Symbolic and mathematical Modultheorie Modulkategorie |
| work_keys_str_mv | AT prestmike purityspectraandlocalisation |